# Dictionary

## exponential notation

In physics, very large and very small numbers are written with the help of powers of the number ten. For large numbers, 10*n* with *n* a non-negative integer is a 1 with *n* trailing zeros:

10^{0} = 1 = one

10^{1} = 10 = ten

10^{2} = 100 = a hundred

10^{3} = 1000 = a thousand

10^{6} = 1,000,000 = a million

10^{9} = 1,000,000,000 = a billion

10^{12} = 1,000,000,000,000 = a trillion

10^{15} = 1,000,000,000,000,000 = a quadrillion

Very small fractions – numbers that differ very little from zero – can be written with the help of 10^{-n}, with n a non-negative integer (n is, again, the number of zeros):

10^{0} = 1 = one

10^{-1} = 0.1 = one tenth

10^{-2} = 0.01 = one hundredth

10^{-3} = 0.001 = one thousandth

10^{-6} = 0.000,001 = one millionths

10^{-9} = 0.000,000,001 = one billionths

10^{-12} = 0.000,000,000,001 = one trillionth

10^{-15} = 0.000,000,000,000,001 = one quadrillionth

Numbers that are not clean powers of ten can be written by factoring out the appropriate powers of ten. For instance,

1748 = 1.748·1000 = 1,748·10^{3},

often written in what is called “scientific notation” as 1.748E3. On the other hand,

0.000,417,55 = 4.1755·10^{-4} = 4.1755E-4.